Mitigating EM Edge Artifacts Using Null-Space Smoothing

The objective of this research is to investigate the potential of total variation (TV) nullspace smoothing to mitigate the edge artifacts produced in expectation maximization (EM) reconstruction. Its success in reducing noise and preserving edges in image restoration, suggests that TV norm minimization could be explored in the reconstruction of positron emission tomography (PET) images. For example, the following criteria could be used for reconstruction: Find the image that has the minimum TV norm such that the measurements produced by the image are sufficiently close to the actual measurements. It is argued here, however, that this criterion may cause distortion of edges because of the Poisson nature of PET measurements. Moreover, the above criterion does not exploit the Poisson model of the data as the EM algorithm does. As a potentially better alternative, TV nullspace smoothing of EM reconstructions is proposed here. Rather than minimizing the whole EM reconstructed image with respect to the TV norm, in nullspace smoothing, only a portion of the reconstructed image is minimized; namely, the nullspace component of the reconstructed image. This may be advantageous because PET data contains no information about the nullspace component of the object being scanned. A second potential advantage stems from the fact that EM algorithm attempts to find an image that maximizes the likelihood function associated with a Poisson model of the data. The nullspace smoothed image is as optimal, in the maximum likelihood sense, as the original unsmoothed image. Methodology. To perform this investigation, noise-less projections of a mathematical phantom were simulated. Results. It was seen that the edge artifacts of the TV nullspace smoothed image were uniformly better than those in the original unsmoothed EM reconstruction. Conclusion. Although the results presented here are encouraging, more work needs to be done in the future to demonstrate the usefulness of nullspace smoothing with real data.